# Highly corrupted image inpainting through hypoelliptic diffusion

arXiv: https://arxiv.org/abs/1502.07331 · HTML: https://mlsanity.com/paper/1502.07331/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2015.

## Built on by (most cited first, 5 of 5)

- [Optimal Transport on the Lie Group of Roto-translations](https://mlsanity.com/paper/2402.15322/) (2024)
- [ChebLieNet: Invariant Spectral Graph NNs Turned Equivariant by Riemannian Geometry on Lie Groups](https://mlsanity.com/paper/2111.12139/) (2021)
- [Sigma Flows for Image and Data Labeling and Learning Structured Prediction](https://mlsanity.com/paper/2408.15946/) (2024)
- [Multi-frequency image completion via a biologically-inspired sub-Riemannian model with frequency and phase](https://mlsanity.com/paper/2110.14330/) (2021)
- [Geometry of the Visual Cortex with Applications to Image Inpainting and Enhancement](https://mlsanity.com/paper/2308.07652/) (2023)

## Abstract (arXiv)

We present a new image inpainting algorithm, the Averaging and Hypoelliptic Evolution (AHE) algorithm, inspired by the one presented in [SIAM J. Imaging Sci., vol. 7, no. 2, pp. 669--695, 2014] and based upon a semi-discrete variation of the Citti-Petitot-Sarti model of the primary visual cortex V1. The AHE algorithm is based on a suitable combination of sub-Riemannian hypoelliptic diffusion and ad-hoc local averaging techniques. In particular, we focus on reconstructing highly corrupted images (i.e. where more than the 80% of the image is missing), for which we obtain reconstructions comparable with the state-of-the-art.